An analogue of convexity for complements of amoebas of varieties of higher codimension, an answer to a question asked by B. Sturmfels.
An estimate of approximation constants for p-adic and real varities.
An extremal property of Rokhlin' s inequality for real algebraic curves.
An inverse mapping theorem for arc-analytic homeomorphisms
We show that a subanalytic map-germ (Rⁿ,0) → (Rⁿ,0) which is arc-analytic and bi-Lipschitz has an arc-analytic inverse.
Analytical representation of ellipses in the Aitchison geometry and its application
Compositional data, multivariate observations that hold only relative information, need a special treatment while performing statistical analysis, with respect to the simplex as their sample space ([Aitchison, J.: The Statistical Analysis of Compositional Data. Chapman and Hall, London, 1986.], [Aitchison, J., Greenacre, M.: Biplots of compositional data. Applied Statistics 51 (2002), 375–392.], [Buccianti, A., Mateu-Figueras, G., Pawlowsky-Glahn, V. (eds): Compositional data analysis in the geosciences:...
Approximation by continuous rational maps into spheres
Investigated are continuous rational maps of nonsingular real algebraic varieties into spheres. In some cases, necessary and sufficient conditions are given for a continuous map to be approximable by continuous rational maps. In particular, each continuous map between unit spheres can be approximated by continuous rational maps.
Approximation of -functions without changing their zero-set
For a function (where is a real algebraic manifold) the following problem is studied. If is an algebraic subvariety of , can be approximated by rational regular functions such that We find that this is possible if and only if there exists a rational regular function such that and g(x) for any in . Similar results are obtained also in the analytic and in the Nash cases.For non approximable functions the minimal flatness locus is also studied.
Arc-analyticity and polynomial arcs
We relate the notion of arc-analyticity and the one of analyticity on restriction to polynomial arcs and we prove that in the subanalytic setting, these two notions coincide.
Around real Enriques surfaces.
We present a brief overview of the classification of real Enriques surfaces completed recently and make an attempt to systemize the known classification results for other special types of surfaces. Emphasis is also given to the particular tools used and to the general phenomena discovered; in particular, we prove two new congruence type prohibitions on the Euler characteristic of the real part of a real algebraic surface.
Artin-Large property for analytic manifolds of dimension two.
Behavior of Welschinger invariants under Morse simplifications
Bernstein and van der Corput-Schaake type inequalities on semialgebraic curves
We show that in the class of compact, piecewise curves K in , the semialgebraic curves are exactly those which admit a Bernstein (or a van der Corput-Schaake) type inequality for the derivatives of (the traces of) polynomials on K.
Betti numbers of random real hypersurfaces and determinants of random symmetric matrices
We asymptotically estimate from above the expected Betti numbers of random real hypersurfaces in smooth real projective manifolds. Our upper bounds grow as the square root of the degree of the hypersurfaces as the latter grows to infinity, with a coefficient involving the Kählerian volume of the real locus of the manifold as well as the expected determinant of random real symmetric matrices of given index. In particular, for large dimensions, these coefficients get exponentially small away from...
Betti numbers of real elliptic surfaces. (Nombres de Betti des surfaces elliptiques réelles.)
Binäre Formen und Primideale.
Bounding the Number of Connected Components of a Real Algebraic Set.
Bounds for the number of connected components and the first Betti number mod two of a real algebraic surface
Calculation of industrial robot trajectory in frame composite production
This article is focused on calculating the trajectory of an industrial robot in the production of composites for the automotive industry. The production technology is based on the winding of carbon fibres on a polyurethane frame. The frame is fastened to the end-effector of the robot arm (i.e. robot-end-effector, REE). The passage of the frame through the fibre processing head is determined by the REE trajectory. The position of the fibre processing head is fixed and is composed of three fibre guide...
Cartan-Chern-Moser theory on algebraic hypersurfaces and an application to the study of automorphism groups of algebraic domains
For a strongly pseudoconvex domain defined by a real polynomial of degree , we prove that the Lie group can be identified with a constructible Nash algebraic smooth variety in the CR structure bundle of , and that the sum of its Betti numbers is bounded by a certain constant depending only on and . In case is simply connected, we further give an explicit but quite rough bound in terms of the dimension and the degree of the defining polynomial. Our approach is to adapt the Cartan-Chern-Moser...
Central Orderings in Fields of Real Meromorphic Function Germs.